# How many universes are there in space

Is there a copy of you reading this article right now? Someone who is not yourself but lives on a planet called Earth, with blue oceans, snow-capped mountains, fertile fields and large cities, part of a solar system with eight other planets? This person's life has been identical to yours in every way so far. But maybe he or she just decides to put this article aside while you read on.

The idea of such a double seems strange and implausible - but obviously we have to get used to this idea, because astronomical observations speak for it. From the simplest - and recently again favored - cosmological model it follows that in an approximately 10 to the power of 10

^{28}Meter distant galaxy a twin of yours lives. This distance is beyond astronomical standards, but that doesn't make your doppelganger any less real. The estimate is based on a simple consideration of probability and does not require speculative modern physics.

According to astronomical observations, space is infinite - or at least sufficiently large - and almost equally filled with matter. In an infinitely large space, even the most unlikely things must happen somewhere. There are an infinite number of other inhabited planets, and not just one but an infinite number of them are inhabited by people who look just like you, have the same name, and have the same memories. These people make every possible variation of your life choices come true.

Most likely, you will never see your doppelgangers. You can see at most the 14 billion light years that light has traveled since the Big Bang. The most distant objects visible today are around 4'10

^{26}Meters away; this distance defines the universe that we can observe, also called Hubble volume, horizon volume or simply our universe. The universes of our doppelgangers are spheres of the same diameter with the planet of our alter ego at their center. This is the simplest example of parallel universes. Each universe is only a small part of a larger "multiverse".

Given this definition, one might think that the concept of the multiverse belongs forever in the realm of metaphysics. But the boundary between physics and metaphysics is defined by whether a theory can be tested experimentally, and not by whether the theory is unfamiliar or contains unobservable things. The boundaries of physics have been expanded further and further and encompass ever more abstract - and formerly metaphysical - terms such as globe, invisible electromagnetic fields, time dilation at high speeds, quantum superpositions, curvature of space and black holes. The multiverse has been on this list for a number of years. It is based on proven theories - in particular the theory of relativity and quantum mechanics - and fulfills both of the basic criteria of an empirical science: It makes predictions and can be falsified. Scientists discuss up to four different types of parallel universes. The question is not whether the multiverse exists, but how many levels it has.

**Level I: Beyond our cosmic horizon**

The parallel universes of your doppelgangers form the Level I multiverse. We all accept the existence of things that we cannot see but that we could observe if we shifted our vantage point or just wait and see like people watching ships appear over the horizon. It is similar with objects beyond our cosmic horizon. The observable universe grows by one light year every year because the light from objects that are increasingly distant has time to reach us. An infinity is out there waiting to be seen. You are probably dead long before your alter ego comes into sight, but in principle - and if the cosmic expansion plays along - your offspring can observe you through a suitably powerful telescope.

The Level I multiverse seems rather trivial. How could space not be infinite? Is there a sign somewhere: "Attention, space ends here"? If so, what would it be? Indeed, Einstein's theory of gravity challenges this naive view. A convexly curved space could very well be finite. A spherical, ring or pretzel-shaped universe would have a finite volume and yet would be unlimited. The cosmic background radiation allows sensitive tests of such models (see "Is space finite?" By Jean-Pierre Luminet, Glenn D. Starkman and Jeffrey R. Weeks, Spektrum der Wissenschaft 7/1999, p. 50). But so far all the indications speak against it. The data fit infinite models much better.

Another possibility would be the earlier popular "island universe": Space is infinite, but matter is limited to a finite area that surrounds us. A variant of this model says that matter becomes thinner over great distances according to a fractal distribution. In both cases, almost all universes in the Level I Multiverse would be empty and dead. However, recent observations of the cosmic microwave background and the galaxy distribution show that matter is distributed very uniformly on a large scale: There are no connected structures larger than approximately 10

^{24}Meter. If this pattern continues, space beyond our observable universe will be teeming with galaxies, stars, and planets.

Beings in level I parallel universes experience the same physical laws as we do - albeit under different initial conditions. Presumably, the matter was distributed so randomly by processes shortly after the Big Bang that all possible arrangements were created with a certain probability. As the cosmologists suspect, our universe with its almost even distribution of matter and its initial density fluctuations of 1 to 100,000 is quite typical - at least for universes that contain observers. This assumption is based on the estimate that your closest identical copy will be 10 to the 10th power

^{28}Meters away. At a distance of around 10 to the 10th power

^{92}Meters, there should be a sphere with a radius of a hundred light years, identical to the one around us, so that any observations we will make over the next hundred years will be entirely consistent with those of our doppelgangers. Around 10 to the 10th

^{118}Meters away from us should be an entire Hubble volume identical to ours.

**The removal of the doppelganger**

These extremely conservative estimates are obtained simply by counting all possible quantum states that a Hubble volume can assume when it is not hotter than 10

^{8}Kelvin. One asks, for example, how many protons fit into a Hubble volume at this temperature. The answer is: 10

^{118}Protons. Since each of these particles may or may not be present, there are 2 to the power of 10

^{118}possible arrangements of protons. A box that contains so many Hubble volumes exhausts all possibilities. Such a container measures roughly 10 to the power of 10

^{118}Meter. Beyond the box, the universes, including ours, must repeat themselves identically. Approximately the same number can also be derived from thermodynamic or quantum gravity theoretical estimates for the entire information content of the universe.

Your next doppelganger is most likely much closer to you than these numbers suggest, as the processes of planet formation and biological evolution greatly improve your chances. Astronomers estimate that our Hubble volume is at least 10

^{20}Contains habitable planets; some of them might well look like the earth.

The concept of the Level I multiverse is constantly used to evaluate theories of modern cosmology - even if the procedure is seldom mentioned explicitly. For example, cosmologists have used the cosmic background to rule out a finite spherical geometry. The hot and cold spots of microwave radiation have a characteristic size that is related to the curvature of the room, and the spots observed seem to be too small for a spherical shape.

Strictly speaking, it is a statistical statement. Since the mean speckle size varies randomly from one Hubble volume to another, our universe could be deceiving us: it could be spherical but happen to have abnormally small speckles. When cosmologists say they ruled out the spherical model with a 99.9 percent probability, they really mean: If this model were correct, less than one in a thousand Hubble volumes would show spots as small as ours.

Obviously, the multiverse theory can be tested and falsified even though we cannot see the other universes. One has to narrow down the ensemble of parallel universes and define a probability distribution - or as mathematicians say, a measure - over this ensemble. Our universe should prove to be particularly likely. Otherwise - if we live in an improbable universe according to the multiverse theory - the theory gets into trouble. As I'll show later, this dimension problem can get pretty complicated.

The Level I multiverse was already a tough piece, but now let's try to imagine an infinite number of separate Level I multiverses. Some may have different spacetime dimensions or different physical constants. These multiverses form a Level II multiverse and are predicted by chaotic perpetual inflation theory.

Inflation, an extension of the Big Bang theory, answers the question of why the universe is so big, so uniform and so flat. Rapid spatial expansion shortly after the Big Bang can explain these and other properties in one fell swoop (see "The self-reproducing inflationary universe" by Andrei Linde, Spektrum der Wissenschaft 1/1995, p. 32). The adjectives "chaotic" and "eternal" refer to what is happening on a large scale. The space as a whole expands and will go on forever, but some areas of space become disconnected and form separate bubbles, similar to the gas bubbles in a rising bread dough. An infinite number of such cosmic bubbles are formed, and each is the seed of a Level I multiverse - infinitely large and filled with matter deposited by the energy field that fueled inflation.

These bubbles are, so to speak, more than infinitely far away from the earth, because one could never reach them, even if one were constantly traveling at the speed of light. The reason is that the space between our bladder and its neighbors is expanding faster than one can traverse it. In principle, our descendants will never see their doubles in level II. By the way, for the same reason: if the cosmic expansion accelerates - as newer observations speak for - you will not even be able to see your alter ego in level I.

**The Level II multiverse**

The level II multiverse is much more varied than level I. The bubbles differ not only in their initial conditions, but also in their supposedly unchangeable natural properties. In modern physics, the prevailing opinion is that the dimensionality of space-time, the properties of elementary particles and many natural constants are not anchored in physical laws, but rather emerged from so-called symmetry breaking. For example, according to one theory, space in our universe originally had nine equal dimensions - but only three of them took part in the cosmic expansion and became the space dimensions we are familiar with. The other six can no longer be observed today because they either remained microscopic and curled up in a ring or because all of the matter only occupies a three-dimensional membrane in the nine-dimensional space. In any case, the original symmetry between the dimensions has been broken. The quantum fluctuations that drive chaotic inflation can cause different symmetry breaks in different bubbles. Some bubbles may become four-dimensional, others contain only two instead of three quark families, and still others may have a stronger cosmological constant than our universe.

A level II multiverse could also emerge from the cyclical creation and destruction of universes. This idea was first investigated scientifically in the 1930s by the physicist Richard C. Tolman and recently refined by Paul J. Steinhardt from Princeton University and Neil Turok from Cambridge University. The Steinhardt-Turok model postulates a second three-dimensional membrane that runs parallel to ours in a higher dimension (see "The invisible dimensions of the universe" by N. Arkani-Hamed et al., Spektrum der Wissenschaft 10/2000, p. 44). This parallel world is actually not really its own universe, because it interacts with ours. But the ensemble of universes past, present, and future that these membranes create forms a multiverse no less diverse than chaotic inflation. The physicist Lee Smolin from the Perimeter Institute in Waterloo (Canadian province Ontario) has come up with another multiverse, the diversity of which corresponds to level II. It does not emerge from membranes, however, but from black holes in which new universes sprout.

**The anthropic principle**

Although we cannot get in contact with other level II parallel universes, their existence can be inferred indirectly, as this explains some strange coincidences in our universe. Here is an "earthly" example: Suppose you go to a large hotel, get the room with the number 1967 and notice that this is the year you were born. What an incredible match you say. But after a moment you don't find the event so surprising anymore. The hotel has hundreds of rooms and you wouldn't have wasted a thought on the room number if you had gotten any other. In other words, even if you didn't know anything about hotels, to explain the consistency you could infer the existence of many other hotel rooms.

Or take the mass of the sun. The mass of a star determines its luminosity, and with simple physics one can calculate that life on earth is only possible if the mass of the sun is in the narrow range between 1.6´10

^{30}and 2,4´10

^{30}Kilograms. Otherwise it would be colder today than Mars or hotter than Venus. The solar mass is 2.0< ´30kilogramm="" –="" auf="" den="" ersten="" blick="" ein="" unglaublicher="" glücksfall.="" die="" sternmassen="" variieren="" zwischen="">

^{29}and 10

^{32}Kilograms, and the chance that the life-friendly value will come out for our sun is extremely small. But as with the hotel example, the coincidence can be explained by postulating an ensemble - in this case a set of planetary systems - and a selection effect, namely the fact that we have to live on a habitable planet. Such an observer-dependent selection effect is called "anthropic". While it is controversial, physicists agree that such selection effects cannot be ignored when reviewing fundamental theories.

What applies to hotel rooms and planetary systems also applies to parallel universes. Most of the properties resulting from symmetry breaking appear to be fine-tuned. If their values were to be changed only a little, a completely different universe would emerge, in which we would probably not be able to exist. If the protons were 0.2 percent heavier, they could decay into neutrons and thus destabilize the atoms. If the electromagnetic force were 4 percent less, there would be neither hydrogen nor stars. If the weak interaction were much weaker, there would be no hydrogen; if it were much stronger, supernovae would not be able to enrich the interstellar medium with heavy elements. And with a much larger cosmological constant, the expansion of the universe would be so rapid that no galaxies could arise.

While the degree of fine-tuning is still being debated, these examples suggest the existence of parallel universes with other physical constants. The theory of the Level II multiverse predicts that physicists will never be able to infer the values of these constants from rationale. They can only calculate probability distributions by taking selection effects into account. The result is only as general as the fact of our existence.

**Level III: Many quantum worlds**

The parallel universes in Levels I and II are so far away that not even astronomers have access to them. But the next level of the multiverse is right under our noses. It comes from the infamous multi-worlds interpretation of quantum mechanics. The idea is that the universe branches into innumerable copies through random quantum processes - one copy for each possible outcome.

At the beginning of the 20th century, the theory of quantum mechanics revolutionized physics by explaining the atomic domain - because it does not obey the classical rules of Newtonian mechanics.Despite the apparent success of the theory, a heated debate broke out over its correct interpretation. The theory no longer describes the state of the universe with classical quantities such as the position and speed of all particles, but with the help of a mathematical object called a wave function. According to the Schrödinger equation, this state develops over time in what mathematicians call "unitary". This means that the wave function rotates in an abstract infinite-dimensional space called Hilbert space. Although quantum mechanics is often characterized as random and indeterminate, the wave function develops deterministically. There is nothing accidental or indeterminate about it.

**"Collapse" of the wave function?**

The problem is how this wave function relates to our observations. Many admissible state functions describe situations that contradict intuition - for example Schrödinger's famous cat, which, as a so-called superposition, is both alive and dead at the same time. In the 1920s, physicists got rid of the problem by postulating that the wave function "collapses" with every observation to a certain classical result. This addition might explain the transition from theory to observation, but it turned an elegant unitary theory into a non-unitary patchwork. The principle of randomness, which is usually ascribed to quantum mechanics, is a result of this postulate.

Over time, many physicists have abandoned this interpretation in favor of another; it was developed by Hugh Everett III in 1957 when he was a PhD student at Princeton University. As he showed, the collapse postulate is unnecessary. Indeed, the unadulterated quantum mechanics does not create any contradictions. Although it says that a classical reality is gradually splitting into superpositions of many such realities, observers subjectively perceive this splitting only as a slight randomness, whereby the probabilities coincide exactly with those of the old collapse postulate. This superposition of classical worlds is the Level III multiverse.

Everett's many-worlds interpretation has been causing confusion within and outside of physics for more than four decades. But it can be grasped quite easily if one distinguishes two points of view when looking at a physical theory: the external point of view of the physicist, who studies his mathematical formulas like a bird overlooking the landscape from high above, and the internal point of view of the observer, the in the midst of the world described by the equations, lives like a frog in the landscape over which the bird flies.

**Bird observatory and frog's eye view**

From a bird's eye view, the Level III multiverse is simple. There is only one wave function. It develops smoothly and deterministically and shows no signs of splitting or parallelism. The abstract quantum world described by this evolving wave function contains a huge number of parallel classical lines of history that continually separate and merge, as well as numerous quantum phenomena that defy classical description. From their frog's perspective, the observer perceives only a tiny part of this overall reality. While they can see their level I universe, a process called decoherence - which simulates the collapse of the wave function without violating unitarity - prevents them from seeing their level III copies. Whenever observers are confronted with a decision and make a choice between the alternatives, quantum effects in their brain lead to a superposition of the results - for example "read the article on" and "put the article aside". From a bird's eye view, this decision-making process causes the person to split into multiple copies: one that reads on and one that stops. From a frog's perspective, however, no alter ego is aware of the other and only notices the branching as a minor randomness - a certain probability of reading further or not.

As strange as this may sound, the exact same situation occurs even in the Level I Multiverse. You obviously made up your mind to keep reading this article, but one of your alter egos in a distant galaxy put the magazine down after the first paragraph. The only difference between Level I and Level III is where your doppelgangers are. On level I, they live somewhere in good old three-dimensional space. In level III they live on another quantum branch of the infinite-dimensional Hilbert space.

The existence of level III depends crucially on the assumption that the temporal development of the wave function is invariably unitary. So far, no deviation from unitarity has been found in the experiment. In recent years it has been confirmed in ever larger systems, including fullerene molecules made up of sixty carbon atoms and kilometers of optical fibers. In theory, unitarity was boosted by the discovery of decoherence (see "100 Years of Quantum Theory" by Max Tegmark and John Archibald Wheeler, Spektrum der Wissenschaft 4/2001, p. 68).

If physics is unitary, the common perception of the role of quantum fluctuations in the Big Bang will have to change. These fluctuations did not accidentally create initial conditions. Rather, they created a quantum superposition of all possible initial conditions that coexisted at the same time. The decoherence then ensured that these initial conditions behaved classically on separate quantum branches. Now comes the crucial point: The distribution of the results on different quantum branches in a certain Hubble volume (level III) is identical to the distribution of the results on different Hubble volumes within a single quantum branch (level I). This property of quantum fluctuations is known as ergodicity in statistical mechanics.

**Nothing new on Level III**

The same consideration applies to level II. The symmetry breaking did not produce a clear result, but a superposition of all results, which quickly went their own way. So if the natural constants, the dimensionality of spacetime and other things can vary between parallel quantum branches on level III, then they also vary between the parallel universes in the multiverse of level II.

In this way, the Level III Multiverse does not add anything new to Level I or II. It just provides more indistinguishable copies of the same universes - the same old stories play out over and over in different quantum branches. The fierce controversy over Everett's theory should therefore calm down quite naturally with the discovery of the equally large but less controversial multiverses of levels I and II.

Still, the consequences are grave and physicists are only just beginning to research them. Take, for example, the question: does the number of universes grow exponentially with time? The surprising answer is no. From a bird's eye view, of course, there is only one single quantum universe. From a frog's perspective, only the universes that can be distinguished at a given point in time count - that is, the noticeably different Hubble volumes in which planets are arbitrarily shifted to other places or they lead a different life. There is 10 to the power of 10 at the quantum level

^{118}Universes whose temperature is below 10

^{8}Kelvin is. This is a huge number, but it is finite.

From a frog's perspective, the evolution of the wave function corresponds to a continuous transition from one of the 10 to the power of 10

^{118}States to the other. Now you are in universe A, where you are reading this sentence - and now you are in universe B, where you are reading this other sentence. Universe B has an observer who is identical to one in Universe A - except for one additional memory. All possible states exist at any moment, and the passage of time is a matter of opinion. Seen in this way, the concept of the multiverse is closely related to the nature of time.

Although the initial conditions and the constants of nature can vary in the multiverses of level I, II and III, the laws of nature remain the same. Why actually? Why shouldn't the laws themselves vary too? What about a universe that only obeys classical physics, without quantum effects? How about if the time did not pass continuously, but in discrete steps like in a computer? Or a universe that is just an empty dodecahedron? In the Level IV multiverse, all of these variants actually exist.

**Level IV: Other mathematical structures**

The surprisingly good correspondence between abstract thinking and reality speaks for the fact that such a multiverse is not just wild speculation. Mathematical structures such as numbers, vectors, equations and geometric objects describe the world with astonishing truthfulness. In a famous lecture in 1959, the physicist Eugene P. Wigner said that the enormous usefulness of mathematics for the natural sciences was almost miraculous. Conversely, mathematical structures appear strangely real. They meet a basic condition for objective existence: they are the same for anyone who studies them. A theorem is true regardless of whether it is proven by a human, a computer, or an intelligent dolphin. Alien civilizations would find the same mathematical structures that we know. Accordingly, the vast majority of mathematicians believe that they do not invent mathematical structures, but discover them.

There are two diametrically opposed opinions about this connection between mathematics and physics, which go back to the ancient philosophers Plato and Aristotle. According to Aristotle, physical reality is fundamental and mathematical language is only a useful approximation. According to Plato, the mathematical structure is actually what is real, which the viewer only partially perceives. In our words: The two philosophers argue about whether the frog's eye view of the observer or the bird's eye view of the laws of nature is fundamental. Aristotle prefers the frog, Plato the bird's eye view.

Children who have never heard of math are spontaneous Aristotelians. The platonic view is only gradually acquired. Theoretical physicists are prone to Platonism: They suspect that mathematics describes the universe so well because it is mathematical in itself. So all of physics is ultimately a mathematical problem. A mathematician with unlimited abilities could, in principle, work out the frog's eye view - that is, which observers with self-confidence the universe contains, what they perceive and which languages they invent to communicate their perceptions to one another.

Let us imagine a world of point-like particles moving around in three-dimensional space. In four-dimensional space-time - the bird's eye view - these particle trajectories resemble a ball of spaghetti. When the frog observes a particle moving at a constant speed, the bird sees a dead straight raw noodle. If the frog has two orbiting particles in front of it, the bird sees two spagetti twisted into a double helix. For the frog, the world is described by Newton's laws for motion and gravity. As a world, the bird has the geometry of the noodles - a mathematical structure. The frog is just a thick ball of noodles, with its complex entanglements corresponding to a composite of particles that is able to store and process information. Our universe is much more complicated than this example, and scientists are still a long way from figuring out which mathematical structure it corresponds to.

**Radical Platonism**

The Platonic paradigm begs the question of why the universe is the way it is. For an Aristotelian, the question is pointless: the universe simply exists. But a Platonist can only wonder why it is precisely this way and not otherwise. If the universe is mathematical in itself, why was only one of the many mathematical structures chosen to describe a universe? Reality seems to harbor a fundamental asymmetry.

As a solution to this riddle, I have suggested that there should be unbroken mathematical symmetry: All mathematical structures also exist physically. Every mathematical structure corresponds to a parallel universe. The elements of this multiverse are not in the same space, but outside of space and time. Most of them probably have no observers. This hypothesis can be seen as a form of radical Platonism because it asserts that the mathematical structures in Plato's world of ideas exist in a physical sense. This is similar to what the cosmologist John D. Barrow of the University of Cambridge called a "heaven of numbers" in his book of the same name and David K. Lewis, the late philosopher at Princeton University, called modal realism. Level IV completes the hierarchy of the multiverses, because every fundamental physical theory can be expressed by a mathematical structure.

The Level IV Multiverse hypothesis makes testable predictions. As in level II, there is also an ensemble - the totality of the mathematical structures - and selection effects. In the course of categorizing mathematical structures, it should turn out that the structure that describes our world is the most general that corresponds to our observations. Likewise, our future observations should be the most general that fit our past, and these in turn the most general that are compatible with our existence.

To quantify this sense of "general" is of course extremely difficult. But an encouraging feature of mathematical structures is that the symmetry and invariance properties that are responsible for the simplicity and order of our universe appear to be general - the rule rather than the exception. Mathematical structures seem to have these properties by themselves, and you have to make complicated additional assumptions to make them disappear.

The scientific theories of the parallel universes form a four-level hierarchy in which the universes become increasingly strange. You can have other initial conditions (level I); other natural constants, elementary particles and symmetries (level II); or even other natural laws (level IV). Strangely enough, Level III of all places has received the most criticism in the last few decades, although it is the only one that does not add qualitatively new universes.

In the coming decade, the drastically improved cosmological measurements of the microwave background and the large-scale distribution of matter will precisely determine the curvature and topology of space, thereby confirming or rejecting Level I. These measurements will also test Level II by testing the chaotic perpetual inflation theory. Advances in astro and particle physics will also clarify how finely tuned the natural constants are, and thus provide arguments for or against level II.

If the attempts to build quantum computers are successful one day, they will provide further clues for level III, because such devices are supposed to use the parallelism of the level III multiverse for parallel computing. On the other hand, some experimenters are also looking for a violation of unitarity - which would exclude level III.

And finally, success or failure in the greatest challenge of modern physics - the union of general relativity and quantum field theory - will determine opinion on Level IV. Either we find a mathematical structure that fits our universe exactly, or we reach a limit for the incredible effectiveness of mathematics. Then we have to give up Level IV.

So should one believe in parallel universes? The main arguments against it are: Firstly, they are wasteful and, secondly, they are extravagant. The first argument is that the theory of the multiverse goes against Ockham's razor - the epistemological thrift of the English theologian Wilhelm von Ockham (1285-1349) - because it postulates the existence of worlds that we can never observe. Why should nature be so wasteful to afford an infinite number of different worlds? But this argument can be reversed in favor of the multiverse. What exactly would nature be wasting? Certainly not space, mass or atoms - the undisputed Level I multiverse already contains an infinite amount of them, so a little more shouldn't matter. But actually it's about the apparent loss of simplicity. The skeptic is bothered by the enormous amount of information that is necessary to describe all these unseen worlds.

**Occam's blunt razor**

But a complete ensemble is often easier to describe than any of its parts. This principle can be expressed by the concept of algorithmic information content. The algorithmic information of a number is roughly speaking the length of the shortest computer program that delivers that number as an output. Let's look at the set of integers: which is simpler, the whole set or a single number? One would intuitively say the single number. But the entire set can be generated with a trivial computer program, while a single number can be of any length.Therefore, the whole set is actually easier.

The set of all solutions to Einstein’s field equations is also simpler than a special solution. The former is described by a couple of equations, while the latter requires the specification of a huge number of initial values on a hypersurface. From this we can see that the complexity increases when we concentrate our attention on a certain element of an ensemble: In doing so, we sacrifice the symmetry and simplicity inherent in the totality of all elements. In this sense, the multiverses of the higher planes are simpler.

When we move from our universe to a Level I multiverse, we no longer need to specify initial conditions. In the transition to level II, there is no need to specify natural constants, and for level IV we no longer have to specify anything. The excess of complexity is only to be found in the subjective perception of the observer - in the frog's eye view. From a bird's eye view, the multiverse couldn't be simpler.

The second accusation - extravagance - is more of an aesthetic than scientific nature and really only makes sense from the Aristotelian point of view. But what did we expect? If we ask a profound question about the nature of reality, shouldn't we expect an answer that seems strange? Evolution has provided us with an intuition for everyday physics that was useful for the survival of our primeval ancestors. We shouldn't be surprised if, beyond the everyday world, the view seems bizarre.

All four levels have in common that the most elegant theory automatically leads to parallel universes. To deny the existence of these universes one has to add experimentally unconfirmed processes and ad hoc assumptions to the theory: finite space, collapse of wave functions, and ontological asymmetry. Ultimately, we have to decide what we find more wasteful and inelegant: many worlds or many words. Perhaps we will gradually get used to the weirdness of our cosmos and find that its extravagance is part of its charm.

**Bibliography**

Inflation, Quantum Cosmology and the Anthropic Principle. By Andrei Linde in: Science and Ultimate Reality: From Quantum to Cosmos. By J.D. Barrow, P.C.W. Davies and C.L. Harper (ed.). Cambridge University Press, 2003.

Our Cosmic Habitat. By Martin Rees. Princeton University Press, 2001.

**Shortly**

- According to recent cosmological observations, parallel universes are not just an extravagant idea. Since space apparently extends infinitely, everything possible is being realized somewhere out there - no matter how improbable. Beyond the range of our telescopes there are regions of space that are identical to ours. The mean distance of such parallel universes can even be calculated.

- From cosmological and quantum physics considerations, researchers conclude on several levels of multiverses with diverse properties and laws of nature. Their existence is able to explain certain peculiarities of our universe and perhaps even to answer fundamental questions - such as the nature of time or the mathematical description of the physical world.

**Space: infinite expanses**

More recent cosmological data indicate that space continues far beyond our observation limits. Recently, the WMAP satellite delivered the most detailed map of fluctuations in the cosmic microwave background to date. The strongest fluctuations are only half an angular degree. This speaks for a flat, infinite space (middle). Only a few cosmologists interpret the "outlier" at the bottom left of the diagram as an indication of a spherical universe with finite volume. In addition, the WMAP data and the galaxy survey 2dF Galaxy Redshift Survey show that the space is evenly filled with matter on a large scale. So other universes should basically be the same as ours.

**The Problem of Probability - What Are Your Chances in the Quadruple Multiverse?**

Although resistance to multiverse theories is gradually waning, the annoying question of how to calculate probabilities in them is growing into a real problem. If there are several identical copies of me, the conventional notion of determinism is no longer good. Even if one knew the entire state of the multiverse, one would not be able to calculate one's future because one cannot determine which copy one is - all copies think they are the original. That is why only probability statements are possible. If a result has a probability of fifty percent, this means that half of all observers observe this result.

Unfortunately, it is not at all easy to calculate which fraction of the infinite number of observers is observing which event. The answer depends on the order in which you count the observers. For comparison: The fraction of whole numbers that are even is fifty percent when sorted numerically (1, 2, 3, 4, ...), but almost one hundred percent when sorted by digits (1, 10, 100, 1000, ...). There is no natural way for observers in separate universes to sort them. Instead, you have to select samples from the universes and weight them with a statistical measure.

This problem can be tamed halfway in level I, becomes serious in level II, is heavily controversial in level III and monstrous in level IV. Alexander Vilenkin from Tufts University dealt with the probability distribution of cosmological parameters for level II. He advocates giving the differently expanded parallel universes statistical weights proportional to their volume. Any mathematician will argue that twice infinite is still infinite. What is the meaning of the statement that an infinite universe expanded by a factor of two has become larger? In addition, a finite ring-shaped universe is equivalent to a perfectly periodic universe with infinite volume - both from a mathematical bird's-eye view and from the frog's-eye view of an observer seated inside. Why should its infinitely smaller volume give it a statistical weight of zero? After all, even in the Level I Multiverse, the Hubble volumes repeat themselves - albeit not periodically, but randomly - after around 10 to the power of 10,118 meters.

But all of this is nothing at all against the problem of assigning statistical weights to the mathematical structures in level IV. Since our universe seems relatively simple, the correct amount could have something to do with complexity.

**The Level I Multiverse**

The simplest type of parallel universe is a region of space that is too far away for our observations. At the moment we can see at most 41026 meters or 42 billion light years. This distance has been covered by light since the Big Bang 14 billion years ago; it is greater than 14 billion light years because cosmic expansion has stretched the distances. Each level I parallel universe is basically the same as our universe. All differences come from variations in the initial distribution of matter.

**How far is a twin universe away?**

Model universe

Let us imagine a two-dimensional universe that only has space for four particles. Such a universe has 24 = 16 possible arrangements of matter. If there are more than 16 of these universes, they must be repeated. The distance to the next repetition is roughly four times the diameter of a universe.

Our universe

The same argument applies to our universe, which has space for around 10118 elementary particles. Therefore, 2 to the power of 10118 arrangements are possible, or around 10 to the power of 10118. Multiplying this by the diameter of the universe results in an average distance to the next duplicate of 10 to the power of 10118 meters.

**The Level II Multiverse**

A more complicated type of parallel universes follows from the theory of cosmic inflation. The level I multiverse - our universe and the neighboring areas of space - is therefore a bubble in an even larger, but largely empty volume. There are other bubbles there that have no connection whatsoever with our world. They condense like raindrops in a cloud. During condensation, variations in the quantum fields endow each bubble with specific properties that distinguish it from other bubbles.

Condensation of the bubbles

A quantum field called inflaton causes space to expand rapidly. Due to random fluctuations, the field loses its power in some spatial regions and the expansion slows down. Bubbles appear in such areas.

Clues

The improbable fine-tuning of the natural forces (middle) and the spacetime dimensions (right) in our universe speaks for the existence of parallel universes of level II. These quantities have just the right values for the creation of life. The most plausible explanation is that these values are the result of chance processes in the creation of our universe, while innumerable other universes exist with different values in which life is not possible.

**The Level III Multiverse**

Quantum mechanics postulates a gigantic number of parallel universes, which, however, are not in the usual space, but in an abstract space of all possible states. Every conceivable state of the world in the context of quantum mechanics corresponds to its own universe. These parallel universes are noticeable in laboratory experiments through typical quantum effects, for example through interference from quantum waves.

Quantum cube

An ideal cube, which is only subject to the laws of quantum mechanics, is placed in a superposition of all six possible throw results with every throw - but an observer only ever sees one of them. To resolve this contradiction, let us imagine that the throw in different universes results in different numbers. In one sixth of all universes the cube shows one, in another sixth two and so on. Since we are trapped in a universe, we can only perceive a fraction of complete quantum reality.

Ergodicity

According to the principle of ergodicity, the quantum mechanical parallel universes are equivalent to less exotic types of parallel worlds. A quantum universe splits into many universes over time. But these new worlds are no different from parallel universes that already exist elsewhere in space - for example other worlds of level I. The basic idea is that all types of parallel universes embody different ways in which events could have happened.

The essence of time

For most people, time is a means of describing change: at one point in time matter is ordered in a certain way, a moment later it is different. The concept of multiverses suggests a different view. If the parallel universes contain every possible arrangement of matter, then time is simply a way of arranging these universes as a sequence. The universes themselves are static, change an illusion.

**The Level IV Multiverse**

The highest form of the multiverse encompasses all conceivable possibilities. His universes differ not only in their location, the cosmological properties or their quantum states, but also in the respective applicable laws of nature. Since these worlds exist outside of space and time, they most closely resemble abstract, static sculptures that stand for the mathematical structure of the applicable physical laws. A simple example is a universe made up of earth, moon and sun that obeys Newton's laws. To an outside observer, this universe appears as a circular ring (earth's orbit), which is wrapped with a ribbon (lunar orbit). Other forms embody other physical laws (a, b, c, d). This approach makes it plausible why our universe can be described mathematically at all.

From: Spektrum der Wissenschaft 8/2003, page 34

© Spektrum der Wissenschaft Verlagsgesellschaft mbH

#### This article is included in Spectrum of Science 8/2003

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